9 problems

Let $u$ be the parameter of the quantum transfer matrix, let $r\geq 1$, and let $a\in\{1,2,\dots,r\}$ and $m\in\mathbb{Z}_{\geq 1}$. Denote by $\widetilde{T}^{(a)}_{m}(v)$ the fuse…

Low-$T$ Bethe root pattern conjecture. All excitations of the quantum transfer matrix at low $T$ and sufficiently large $N$ can be parametrised in this way, and, up to corrections…

Let $N$ be the even Trotter number, let $u_N$ be the corresponding Trotter parameter, and let $r$ be the rank parameter of the $U_q(\widehat{sl(r+1)})$ model. Let $M_a$ denote the…

Let $R(v)$ be the row-to-row transfer-matrix $R$-matrix, let $\widetilde{R}(v)$ be its $90$-degree rotation, and let $t_{\mathrm{QTM}}(v)$ be the quantum transfer matrix acting on…

Let $0<\zeta<\pi$ be generic, let ${\mathfrak{s}}\in\mathbb Z$, and let $1=r_1<\dots<r_p$ be the allowed thermal string lengths. Consider a solution…

Low-temperature spectrum completeness conjecture. Running over all such values of $k$ should produce every possible choice of the integers $n_p^{(\sigma)}=n_h^{(\sigma)}$,…

Consider the XXZ chain in the antiferromagnetic massive regime at finite magnetic field and low temperature. Let the eigenvalue ratios of the quantum transfer matrix be those obtai…

Let the XXZ chain be in the antiferromagnetic massive regime at finite magnetic field and sufficiently low temperature. The quantum transfer matrix has eigenstates, and the higher-…

Consider the isotropic Heisenberg chain at finite temperature and vanishing magnetic field. Let $\gamma(\mu_1,\mu_2)$ be defined by … where $\Lambda(\mu_2,\mu_1)$ is the largest ei…